It's the state that ends with "oh crap, I'm supposed to be meditating." It's the quality you commonly experience while daydreaming, or any time your default network is active. And it's a state that negative emotions are great at sucking you into.
While you're meditating and trying not to generate thoughts, still they arise. This should make it clear that "you" are not the originator of all of your thoughts. When you're off-cushion and a particularly strong negative emotion happens your way, chances are it will do some damage before you gather your wits and evict it. In a mild case, the damage may simply be a mild unease for some minutes or hours. The longer you let it sideline your mind, though, the more thorough the roots it will lay down, and the harder it is to escape cleanly from.
One reason to practice nondistractedness (aka meditation) is that you'll be more frequently on your guard during the day. And don't scold yourself for every thought that distracts you on the cushion, for every return to your object strengthens your ability to "snap out of it" when in the clutches of any experience you'd like to escape.